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We define a new geometric object--the stack of local systems with restrictedvariation. We formulate a version of the categorical geometric Langlandsconjecture that makes sense for any constructible sheaf theory (such as l-adicsheaves). We formulate a conjecture that makes precise the connection betweenthe category of automorphic sheaves and the space of automorphic functions.

The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support